论文标题
对M. Pellegrini和P. Shumyatsky的猜想的反例
Counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky
论文作者
论文摘要
在本文中，我们为M. Pellegrini和P. shumyatsky的猜想提供反例，这些猜想指出，除非$ g = \ text {psl}（n，2）$ n \ n for $ n \ geq 4 $，否则在有限的非亚伯利亚简单组中的中心符中的每个coset都包含一个奇数元素。更确切地说，我们表明，对于所有$ n \ geq 2 $，对交替的组$ a_ {8n} $不满意。
In this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset of the centralizer of an involution in a finite non-abelian simple group $G$ contains an odd order element, unless $G=\text{PSL}(n,2)$ for $n\geq 4$. More precisely, we show that the conjecture does not hold for the alternating group $A_{8n}$ for all $n\geq 2$.
